Prime, irreducible, and completely irreducible lattice preradicals on modular complete lattices (I)
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© 2022 World Scientific Publishing Company.Based on the concept of a lattice preradical recently introduced in [T. Albu and M. Iosif, Lattice preradicals with applications to Grothendieck categories and torsion theories, J. Algebra 444 (2015) 339-366], we present and investigate in this paper, the latticial counterparts of the concepts of prime and irreducible preradicals on the category Mod-R of all unital right R-modules over an associative ring R with identity, introduced and studied in [F. Raggi, J. Ríos Montes, H. Rincón, R. Fernández-Alonso and C. Signoret, Prime and irreducible preradicals, J. Algebra Appl. 4 (2005) 451-466].
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